I'm watching the History Channel show "Vikings", and from what it sounds like, the people of Europe (specifically England) hadn't the faintest idea of Scandinavia or that people lived there until raiding began. Is that accurate? Was the reverse also true?
It's not at all accurate. Elites across Northern Europe had long based their power on an ability to maintain and control long-distance connections. During the Roman Period, these connections gravitated toward the Mediterranean, whether through official ties as in Roman Britain, or through diplomatic, economic, and even mercenary ties as in 'barbarian' Scandinavia. The collapse of Western Roman imperial power in the mid-400s removed this center of gravity, but long-distance ties were still valued.
Interestingly, the influential archaeologist Lotte Hedeager has claimed that as the Huns briefly supplanted Roman power in central Europe during the 450s, people around the Baltic began looking to the Huns for new cultural cues. This catalyzed the development of a new intellectual, political, and artistic culture that eventually flourished into Norse society as we understand it today. This view, however, is only one perspective and by no means represents a scholarly consensus. It does, however, help explain why the earliest examples of "Viking" myths often can be dated to this period.
In central Sweden, this new culture began to focus on military elites and naval power, best seen in massive mound burials. Interestingly, at least one powerful family in eastern England seems to have been directly tied into these developments. Similar massive boat burials can be found north of London at Sutton Hoo as well as north of Stockholm at places like Vendel, Valsgärde, and Uppsala. The richness of this culture intrigued, among others, JRR Tolkien, who relied upon it as part of his inspiration for the Riders of Rohan, and it seems also to have influenced Peter Jackson's representation of Rohan in the film versions of The Lord of the Rings.
These types of cemeteries flourished into the early 600s, after which it seems like trading towns gradually replaced aristocratic halls as the foci for long-distance connections. Evidence from these early "urban" sites, however, suggests that trade was often coastal and depended on relatively short legs between travel hubs. So if the elites of Sutton Hoo were really connected to those of central Sweden, it probably meant several weeks of travel sticking close to the shore.
There were, nevertheless, several major changes leading up to the Viking Age that prepared the way for a dramatically different situation. Climate fluctuations, which had corresponded with the fall of Roman imperial power in the west, gradually stabilized. This meant that kings could now aggregate more landed wealth, and agricultural surplus went to feed a new literary elite—the kinds of churchmen who would later complain about viking raiding. The new climate also meant a wetter central and northern Europe, encouraging maritime and riverine trade.
At about the same time larger warships and traders began taking advantage of wind power and reintroduced the sail to northern shipping. A lack of evidence prevents us from pinpointing when the transition from rowing to sailing occurred, but perhaps in the mid-700s. The return of the sail made overnight voyages risky and perhaps generally avoided, but nevertheless increasingly possible. Suddenly, Norway was a few days direct travel from Britain, rather than a multi-week coastal circuit.
So by the late 700s, we have an increasingly maritime society circulating the North Sea, surplus wealth accumulating in Western Europe, and a community of authors ready to complain if they find themselves in danger of losing access to that surplus. And thus—in AD 793 as a churchman in Francia wrote to offer condolences to fellow monks recently plundered at their wealthy monastery of Lindisfarne by a small band of pirates who had made the few-days sail direct from Norway—the Viking Age was born. Not at all how the History Channel shows it, but at least there aren't any aliens.
Steven Ashby, "What Really Caused the Viking Age? The Social Content of Raiding and Exploration," Archaeological Dialogues 22.1 (2015): 89–106.
James Barrett, "Rounding Up the Usual Suspects: Causation and the Viking Age Diaspora," in Atholl Anderson, James H. Barrett, and Katherine V. Boyle, eds., The Global Origins and Development of Seafaring (Cambridge: McDonald Institute for Archaeological Research, 2010), 289–302.
Robin Fleming, Britain after Rome: The Fall and Rise, 400–1070 (London: Allen Lane, 2010).
Lotte Hedeager, Iron Age Myth and Materiality: An Archaeology of Scandinavia, AD 400-1000 (London: Routledge, 2011).
Christopher Loveluck, Northwest Europe in the Early Middle Ages, c. AD 600–1150 (Cambridge: Cambridge University Press, 2013).